Optimal Control Algorithm for Stochastic Systems with Parameter Drift

Abstract

A novel optimal control problem is considered for multiple input multiple output (MIMO) stochastic systems with mixed parameter drift, external disturbance and observation noise. The proposed controller can not only track and identify the drift parameters in finite time but, furthermore, drive the system to move towards the desired trajectory. However, there is a conflict between control and estimation, which makes the analytic solution unattainable in most situations. A dual control algorithm based on weight factor and innovation is, therefore, proposed. First, the innovation is added to the control goal by the appropriate weight and the Kalman filter is introduced to estimate and track the transformed drift parameters. The weight factor is used to adjust the degree of drift parameter estimation in order to achieve a balance between control and estimation. Then, the optimal control is derived by solving the modified optimization problem. In this strategy, the analytic solution of the control law can be obtained. The control law obtained in this paper is optimal because the estimation of drift parameters is integrated into the objective function rather than the suboptimal control law, which includes two parts of control and estimation in other studies. The proposed algorithm can achieve the best compromise between optimization and estatimation. Finally, the effectiveness of the algorithm is verified by numerical experiments in two different cases.

Advanced Vibration-Based Fault Diagnosis and Vibration Control Methods

“…This Special Issue on “Advanced Vibration-Based Fault Diagnosis and Vibration Control Methods” includes twelve papers ranging across different methods used in the electrical and mechanical industries’ systems. The papers include a good literature review of the current new works on the verification of mechanical properties identification based on the impulse excitation technique and mobile device measurements [ 4 ], the method for bearing fault diagnosis under variable speeds based on envelope spectrum fault characteristic frequency band identification [ 5 ], the interface design of head-worn display applications for condition monitoring in aviation [ 6 ], color recurrence plots for bearing fault diagnoses [ 7 ], the failure mode detection and validation of a shaft-bearing system with common sensors [ 8 ], the strain response and buckling behavior of composite cylindrical shells subjected to external pressure with one end fixed and the other free of boundary conditions [ 9 ], the smartphone-based and data-driven superstructure state prediction method for highway bridges in service [ 10 ], the optimal control algorithm for stochastic systems with parameter drift [ 11 ], the nonlinear vibration control experimental system design of a flexible arm using interactive actuations from shape memory alloy [ 12 ], the design of an active vibration isolation controller with a disturbance observer-based linear quadratic regulator for optical reference cavities [ 13 ], the applicability of touchscreens in manned/unmanned aerial vehicle cooperative missions [ 14 ], and the engineering frequency domain analysis and vibration suppression of flexible aircraft based on an active disturbance rejection controller [ 15 ].…”

“…For the gyroscope in a satellite, if its drift parameters are accurately detected at any time, the drift could be obtained; then, related measures could be used to reduce accidents. Zhang et al [ 11 ] presented an optimal control method for a stochastic system with multiple inputs and multiple outputs by considering the observation noise, external disturbance, and mixed parameter drift. The method can identify and track the drift parameters in a finite time.…”